76 citations · 117 across the 10 of their papers we have counts for
10 papers
Precise asymptotics at the tip of the Mandelbrot set
Neil Dobbs, Jacek Graczyk, Nicolae Mihalache
For the quadratic family , the only parameters in the Mandelbrot set for which the Julia set has Hausdorff dimension are and . Nea…
Hausdorff dimension of Julia sets in the logistic family
Neil Dobbs, Jacek Graczyk, Nicolae Mihalache
A closed interval and circle are the only smooth Julia sets in polynomial dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia sets close to the circle depe…
Analytic structures and harmonic measure at bifurcation locus
Jacek Graczyk, Grzegorz Świątek
We study conformal quantities at generic parameters with respect to the harmonic measure on the boundary of the connectedness loci for unicritical polynomials $f_c(z)=…
Metric properties of mean wiggly continua
Jacek Graczyk, Peter W. Jones, Nicolae Mihalache
We study lower and upper bounds of the Hausdorff dimension for sets which are wiggly at scales of positive density. The main technical ingredient is a construction, for every conti…
Non-uniform hyperbolicity in complex dynamics
Jacek Graczyk, Stanislav Smirnov
We study rational functions satisfying summability conditions - a family of weak conditions on the expansion along the critical orbits. Assuming their appropriate versions, we deri…
Metric attractors for smooth unimodal maps
Jacek Graczyk, Duncan Sands, Grzegorz Swiatek
We classify the measure theoretic attractors of general C^3 unimodal maps with quadratic critical points. The main ingredient is the decay of geometry.